Write changes to XMP first (That's for everyone, even if you're not moving files!):
Note that before you move any files... indeed, before you do anything with lightroom ever again, from this moment forward, do this, first: Catalog Settings > Metadata > Automatically write changes into XMP -- that means that in addition to storing your edits in the lightroom catalog, they get stored inside the DNG as well, or in a sidecar file if you're using PEF, I think -- I'm not. which means that if your lightroom catalog ever gets corrupted, you can start a new one from scratch and you won't lose any of your edits. You'll lose the *history* where you can go back and see a step-by-step list of your edits in the order you did them, but that's a lot better than losing all the work you put into perfecting an image.
Now, if you've already done that and waited for it to complete updating all the photos, make a backup copy of your catalog just to be safe, and proceed.
A note on "conventional wisdom"
Conventional wisdom says that the only safe way to move photos in lightroom is from within lightroom itself. Anytime you move photos from outside Lightroom, LR gets confused and can't find the photos, and if you click on a moved photo, it'll prompt you to find its new location, and you can tell it to find neighboring photos that were relocated as well.
That's great, I guess, if you're moving a really small number of photos, but there's a much, much faster and better way to do it if you're looking at more than a few hundred shots. I just moved around 100K mostly raw images to a NAS because I was running out of space on my 1TB local drive and 2TB external drives. Doing that in lightroom would have been impossible. It doesn't handle any network hiccups well, and it's ridiculously slow as a file transfer device.
Copying files reliably & quickly outside of Lightroom
Instead, on a mac (windows would be the same technique but a different command line tool, like RoboCopy instead of rsync), run this from Terminal (updated with the correct paths for your storage locations, of course):
sudo rsync -aE --progress /Volumes/SourceDrive/PhotosParentFolder/ /Volumes/DestinationDrive/PhotosParentFolder/
That's going to mirror the contents of SourceDrive onto DestinationDrive, and if anything happens and it stops running, you can start it again, and it will pick up where you left off. Depending on how many files, how large they are, how fast your network and your drives are, that can take a while. Copying a terabyte isn't fast, even over a gigabit network, but with this, you can restart it later and the only time you lose is the time it spends compiling a list of the files involved & checking if they've already been copied.
Once it finishes running, it will give a report noting any files it couldn't copy for any reason, you can run it again or copy them by hand if necessary).
Telling Lightroom where to find them
Next, just open up lightroom, go into the Folders menu, right click on the original folder, and choose "Update Folder Location". If you've already wiped the photos off of your SourceDrive, you can still do this, but instead of "update folder location" it'll say "find missing folder".
This is far, far superior to doing it on an individual photo and then telling it to find nearby missing photos as the video displays - updating individual missing photos can take many hours (I don't know why, but that "nearby missing photos" command is incredibly slow to actually update said nearby folders), even if you kept them all in a single folder, and it will only work within the folder the image is in, which in many people's cases will be a single day's shots.
Doing it with the "find missing folder" tool, they all get updated at once, and if you do it from a parent folder (example: My setup is like "Photos/2016/2016-10-12/filename.dng"), it will cover any subfolders, as well, if they were also moved. In my case, moving photos going back to 2007 took 1 right click and "update folder location" or "find missing folder" for each year folder. And it handles merging nicely, too - I had January through September of 2015 on the external drive and October-December of 2015 on my local drive, for example, and when I did the second 2015 "Update folder location" it mentioned that there was already a folder by that name in my destination, and asked if I wanted to merge them. I said yes, and it did so without complaint.
Deleting the original folders
And after you've verified that files are accessible, you can delete the old folders. I usually leave them in place for a week or so just in case, though. Better safe than sorry.